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  2. Self-balancing binary search tree - Wikipedia

    en.wikipedia.org/wiki/Self-balancing_binary...

    Most operations on a binary search tree (BST) take time directly proportional to the height of the tree, so it is desirable to keep the height small. A binary tree with height h can contain at most 2 0 +2 1 +···+2 h = 2 h+1 −1 nodes. It follows that for any tree with n nodes and height h: + And that implies:

  3. Tree (abstract data type) - Wikipedia

    en.wikipedia.org/wiki/Tree_(abstract_data_type)

    In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, [ 1 ] [ 2 ] except for the root node, which has no parent (i.e., the ...

  4. Weight-balanced tree - Wikipedia

    en.wikipedia.org/wiki/Weight-balanced_tree

    If the two trees have the balanced weight, Join simply create a new node with left subtree t 1, root k and right subtree t 2. Suppose that t 1 has heavier weight than t 2 (the other case is symmetric). Join follows the right spine of t 1 until a node c which is balanced with t 2.

  5. Binary tree - Wikipedia

    en.wikipedia.org/wiki/Binary_tree

    A labeled binary tree of size 9 (the number of nodes in the tree) and height 3 (the height of a tree defined as the number of edges or links from the top-most or root node to the farthest leaf node), with a root node whose value is 1. The above tree is unbalanced and not sorted.

  6. AVL tree - Wikipedia

    en.wikipedia.org/wiki/AVL_tree

    If the two trees differ by height at most one, Join simply create a new node with left subtree t 1, root k and right subtree t 2. Otherwise, suppose that t 1 is higher than t 2 for more than one (the other case is symmetric). Join follows the right spine of t 1 until a node c which is balanced with t 2.

  7. Binary search tree - Wikipedia

    en.wikipedia.org/wiki/Binary_search_tree

    Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.

  8. Optimal binary search tree - Wikipedia

    en.wikipedia.org/wiki/Optimal_binary_search_tree

    Unlike splay trees and tango trees, Iacono's data structure is not known to be implementable in constant time per access sequence step, so even if it is dynamically optimal, it could still be slower than other search tree data structures by a non-constant factor. The interleave lower bound is an asymptotic lower bound on dynamic optimality.

  9. Tree traversal - Wikipedia

    en.wikipedia.org/wiki/Tree_traversal

    In computer science, tree traversal (also known as tree search and walking the tree) is a form of graph traversal and refers to the process of visiting (e.g. retrieving, updating, or deleting) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited.